Accumulator models

Word acquisition as a continuous process of lexical consolidation (Hidaka 2013; Mollica and Piantadosi 2017)

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For participant \(i\) and word \(j\):

Including learning instances from parallel activation

\[ \begin{aligned} \text{Learning instances}_{ij} &= Age_i \cdot Frequency_j + \\ &(Similarity_j \cdot \text{Learning instances}_{ij'}) \end{aligned} \]

Catalan-Spanish bilingual (no parallel activation)

Catalan-Spanish bilingual (parallel activation)

Questionnaire

• On-line (formr, Arslan, Walther, and Tata 2020), inspired in MacArthur-Bates CDI (Fenson et al. 1994)

• ~1,600 items/words (800 Catalan + 800 Spanish)

• Participants filled one of four versions of the questionnaire:

• 500 items: 250 Catalan + 250 Spanish

• Short-listed (nouns): 302 translation equivalents (TE)

Participants

Modelling

Model structure

Ordinal regression model: \(P(Understands)\), \(P(Says)\)

• No < Understands < Understands and Says

Multilevel: Crossed-random effects

• Participant and Translation equivalent as grouping variables

Bayesian: probability of parameter values

\[P(\text{model} | \text{data}) \propto P(\text{data} | \text{model}) \times P(\text{model})\]

Predictors

Posterior distribution

Posterior predictions

Appendix

Item properties

Levenshtein similarity

Phonological similarity

Levenshtein distance: number of edits for two character strings to become identical

Levenshtein similarity

\[ 1-\frac{lev(A, B)}{Max(length(A), length(B))} \]